A339434 Number of compositions (ordered partitions) of n into a prime number of distinct prime parts.

0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 8, 0, 8, 2, 8, 8, 10, 0, 16, 8, 16, 14, 16, 12, 18, 14, 22, 18, 136, 18, 138, 26, 22, 26, 258, 30, 266, 30, 266, 158, 492, 36, 506, 158, 510, 278, 744, 174, 748, 290, 758, 528, 990, 306, 1228, 668, 1116, 780, 6384, 678, 6630, 800, 1720, 1274

Offset

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Index entries for sequences related to compositions

Example

a(10) = 8 because we have [7, 3], [3, 7], [5, 3, 2], [5, 2, 3], [3, 5, 2], [3, 2, 5], [2, 5, 3] and [2, 3, 5].

Maple

s:= proc(n) option remember; `if`(n<1, 0, ithprime(n)+s(n-1)) end:
b:= proc(n, i, t) option remember; `if`(s(i)<n, 0,
      `if`(n=0, `if`(isprime(t), t!, 0), (p->`if`(p>n, 0,
         b(n-p, i-1, t+1)))(ithprime(i))+b(n, i-1, t)))
    end:
a:= n-> b(n, numtheory[pi](n), 0):
seq(a(n), n=0..70);  # Alois P. Heinz, Dec 04 2020

Mathematica

s[n_] := s[n] = If[n < 1, 0, Prime[n] + s[n - 1]];
b[n_, i_, t_] := b[n, i, t] = If[s[i] < n, 0,
     If[n == 0, If[PrimeQ[t], t!, 0], Function[p, If[p > n, 0,
       b[n - p, i - 1, t + 1]]][Prime[i]] + b[n, i - 1, t]]];
a[n_] := b[n, PrimePi[n], 0];
Table[a[n], {n, 0, 70}] (* Jean-François Alcover, Mar 01 2022, after Alois P. Heinz *)

Crossrefs

Cf. A000040, A045450, A052467, A085755, A085756, A102623, A219107.

Sequence in context: A207944 A063088 A101276 * A348325 A103863 A166395

Adjacent sequences: A339431 A339432 A339433 * A339435 A339436 A339437

Keyword

nonn,look

Author

Ilya Gutkovskiy, Dec 04 2020

Status

approved